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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Complex Numbers

Grade: 10-a Lesson: S2-L8

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Divide the complex numbers: \$(6 + 3i) / (2 + i)\$ .
2	Step	To divide the complex numbers	\$(6 + 3i) / (2 + i)\$
3	Step	We can use the process of multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of a complex number a + bi is a − bi.
4	Step	To find the conjugate of the denominator (2 + i), simply change the sign of the imaginary part to get 2 - i	\$(6 + 3i) / (2 + i) times (2 - i) / (2 - i) \$
5	Step	Now, perform the multiplication in both the numerator and denominator:	\$ ( 12 - 6i + 6i - 3i^2 ) / ( 4 - 2i + 2i - i^2) = (12 - 3i^2) / (4 - i^2)\$
6	Step	Simplify terms with \$i^2\$ (where \$i^2 = -1\$), then simplify	\$ ( 12 + 3) / ( 4 + 1 )\$
7	Step	So, the result is	\$ 15/5 = 3 \$
8	Step	So, the division of the complex numbers \$(6 + 3i) / (2 + i)\$ is equal to 3.
9	Choice.A	This is the accurate result of the division	3
10	Choice.B	This is wrong. The result of the division is not negative it’s a positive	-2
11	Choice.C	This is not correct because the calculation results in 3, not 6	6
12	Choice.D	This is incorrect because, as we’ve shown, the division yields a non-zero complex number, specifically 3	0
13	Answer	Option	A
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Divide the complex numbers: \$(6 + 3i) / (2 + i)\$ .

Step

To divide the complex numbers

\$(6 + 3i) / (2 + i)\$

Step

We can use the process of multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of a complex number a + bi is a − bi.

Step

To find the conjugate of the denominator (2 + i), simply change the sign of the imaginary part to get 2 - i

\$(6 + 3i) / (2 + i) times (2 - i) / (2 - i) \$

Step

Now, perform the multiplication in both the numerator and denominator:

\$ ( 12 - 6i + 6i - 3i^2 ) / ( 4 - 2i + 2i - i^2) = (12 - 3i^2) / (4 - i^2)\$

Step

Simplify terms with \$i^2\$ (where \$i^2 = -1\$), then simplify

\$ ( 12 + 3) / ( 4 + 1 )\$

Step

So, the result is

\$ 15/5 = 3 \$

Step

So, the division of the complex numbers \$(6 + 3i) / (2 + i)\$ is equal to 3.

Choice.A

This is the accurate result of the division

Choice.B

This is wrong. The result of the division is not negative it’s a positive

-2

Choice.C

This is not correct because the calculation results in 3, not 6

Choice.D

This is incorrect because, as we’ve shown, the division yields a non-zero complex number, specifically 3

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?